Opiates more potent than heroin (Hydro/Oxy-morphone specifically) tend to have a similar "rush", while not retaining the same level of euphoria/calmness/etc. AFTER the rush that one does from something such as heroin or moprhine. Though I'm definitely not sure, I'd guess that drugs such as dilaudid and numorphan have shorter half-lifes than heroin (which has a half-life of two minutes).
As to why they are used medically:
While they don't retain the euphoria that heroin does, they are much more potent as analgesics, making it much more valuable to doctors (as much of today's professional world of medicine seems to consider anything that makes you feel good to be bad).
-john